Solving nonlinear time-dependent diffusion equations with the dual reciprocity method in Laplace space

Engineering Analysis with Boundary Elements

Volumn 18, Issue 1, 1996, Pages 19-27

  Zhu, Songping ^a   Satravaha, Pornchai ^a  

^a UNIVERSITY OF WOLLONGONG   (Australia)

Author keywords

Boundary element method; Dual reciprocity method; Laplace transform; Nonlinear time dependent diffusion problems

Indexed keywords

LAPLACE TRANSFORM DUAL RECIPROCITY METHOD (LTDRM); NONLINEAR TIME DEPENDENT DIFFUSION EQUATIONS;

BOUNDARY ELEMENT METHOD; LINEARIZATION; NONLINEAR EQUATIONS; PROBLEM SOLVING; TIME DOMAIN ANALYSIS;

LAPLACE TRANSFORMS;

EID: 0030181501     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0955-7997(96)00034-3     Document Type: Article

References (17)

1. Zhu, S., Zhang, Y. & Marchant, T. R. A DRBEM model for microwave heating problems. Appl. Math. Modelling, 1995, 19, 287-297.
2. Partridge, P. W. & Wrobel, L. C. The dual reciprocity boundary element method for spontaneous ignition. Int. J. Num. Meth. Engng, 1990, 30, 953-963.
3. Sudicky, E. A. The Laplace transform Galerkin technique: a time-continuous finite element theory and appliction to mass transport in groundwater. Water Resources Res., 1989, 25 (8), 1833-1846.
4. Evans, D. J. Alternating group explicit method for the diffusion equation. Appl. Math. Modelling, 1985, 9, 201-206.
5. Bruch, J. C. & Zyvoloski, G. Transient two-dimensional heat conduction problems solved by the finite element method. Int. J. Num. Meth. Engng, 1974, 8, 481-494.
6. Curran, D. A. S., Lewis, B. A. & Cross, M. A boundary element method for the solution of the transient diffusion equation in two dimensions. Appl. Math. Modelling, 1986, 10, 107-113.
7. Brebbia, C. A., Telles, J. C. F. & Wrobel, L. C. Boundary Element Techniques. Springer-Verlag, Berlin, 1984.
8. Zhu, S. & Zhang, Y. Solving general field equations in infinite domains with dual reciprocity boundary element method. Engng Anal. Boundary Elements, 1993, 12 (4), 241-250.
9. Moridis, G. J. & Reddell, D. L. The Laplace transform boundary element (LTBE) method for the solution of diffusion-type equations. In Boundary Elements XIII. Computational Mechanics Publication, Southampton, 1991, pp. 83-97.
10. Nardini, D. & Brebbia, C. A. A new approach for free vibration analysis using boundary elements. In Boundary Element Methods in Engineering, ed. C. A. Brebbia. Springer-Verlag, Berlin, 1982, pp. 312-326.
11. Zhu, S., Satravaha, P. & Lu, X. Solving the linear diffusion equations with the dual reciprocity method in Laplace space. Engng. Anal. Boundary Elements, 1994, 13 (1), 1-10.
12. Wrobel, L. C. & Brebbia, C. A. The dual reciprocity boundary element formulation for nonlinear diffusion problems. Camp. Method Appl. Mech. Engng, 1987, 65, 147-164.
13. Satravaha, P., Lu, X. & Zhu, S. A combined Laplace transform dual reciprocity boundary formulation for transient heat conduction problems. Proceedings of the Fifth Australasian Heat and Mass Transfer Conference, Brisbane, Australia, 1993, pp. 21.1-21.6.
14. Satsuma, J. Exact soultions of Burgers' equation with reaction terms. In Topics in Soliton Theory and Exactly Solvable Nonlinear Equations, ed. M. Ablowitz, B. Fuchssteiner and M. Kruskal. World Scientific, Singapore, 1987, pp. 255-262.
15. Stehfest, H. Algorithm 368: numerical inversion of Laplace transform. Commun. ACM, 1970, 13, 47-49, 624.
16. Partridge, P. W., Brebbia, C. A. & Wrobel, L. C. The Dual Reciprocity Boundary Element Method. Computational Mechanics Publications, Southampton, 1992.
17. Frank-Kamenetskii, D. A. Diffusion and Heat Exchange in Chemical Kinematics. Princeton University Press, Princton, NJ, 1955.